The Metaphysics of Causation

What must a world be like, to host causal relations? When the cue ball
knocks the nine ball into the corner pocket, in virtue of what is this
a case of causation?

Questions about the metaphysics of causation may be usefully divided
into questions about the causal relata, and questions about the causal
relation. Questions about the causal relata include the questions of
(1.1) whether they are in spacetime (immanence), (1.2) how
fine-grained they are (individuation), and (1.3) how many
there are (adicity). Questions about the causal relation
include the questions of (2.1) how causally related and causally
unrelated sequences differ (connection), (2.2) how sequences
related as cause to effect differ from those related as effect to
cause or as joint effects of a common cause (direction), and
(2.3) how if at all sequences involving causes differ from those
involving mere background conditions (selection).

Philosophers have, of course, disagreed over all of these
questions. In what follows, I shall survey some of the main arguments
in the literature.

Question: What are the causal relata? When the cue
ball knocks the nine ball into the corner pocket, what are the terms
of this causal relation? An account of the causal relata should
reveal what sort of thing they are, how many of them there are, and
what job each does. In short, it should reveal their
category, number, and role.

Options: The standard view of the causal relata is
that they are of the category of event, and that their number
is two, in the roles of cause and
effect. So on the standard view, when the cue ball knocks the
nine ball into the corner pocket, there is said to be an (actual)
event e1 of the cue ball striking the nine ball,
and an (actual, distinct) event e2 of the nine
ball sinking into the corner pocket, such that e1
is cause and e2 effect. The standard view, in
short, holds that the causal relata are a pair of events.

The standard view has, of course, been disputed on all counts. As to
category, while the standard view casts the causal relata as events
(Davidson 1980a and 1980b, Kim 1973, Lewis
1986b), one also finds considerable support for facts
(Bennett 1988, Mellor 1995), and occasional support for
such other entities as features (Dretske 1977),
tropes (Keith Campbell 1990), states of affairs
(Armstrong 1997), situations (Menzies 1989a), and
aspects (Paul 2000). Allegiances are further
complicated by disagreements over what events, facts, and these other
creatures are.

As to number and role, while the standard view numbers the causal
relata at two (Davidson 1980b, Mackie 1965, Lewis 1986a), one finds
some support for contrastive views featuring three and even
four relata (Hitchcock 1996, Woodward 2003, Maslen 2004,
Schaffer 2005, Menzies 2007, Northcott 2008, Weslake forthcoming) with
the additional term(s) playing the roles of causal
alternative and/or effectual difference. One also finds
some support for additional relata of a different sort, including
descriptions (Anscombe 1975, McDermott 1995), models
(Menzies 2004, Halpern and Pearl 2005, Hitchcock 2007a), and/or
default states (Menzies 2004, McGrath 2005, Hall 2007,
Hitchcock 2007a, Halpern 2008). (In what follows I will reserve
“the relata” for events or facts or whatnot, and use
“secondary relata” when I wish to speak of the prospect of
descriptions or models or defaults as additional relata. This is
purely for expository convenience.)

Category: What is the category of the causal relata?
What sort of thing are they? An account of the category of the relata
should first determine which characteristics differentiate events from
facts from the others, and then identify which characteristics the
relata must have.

In practice, there are two main differentiating characteristics that
one finds invoked. The first is immanence. Events and the
others are generally regarded as immanent, while facts are generally
regarded as transcendent. That is, the event of Brutus's stabbing
Caesar is something concrete that occurs at a particular
spatiotemporal location (the Senate on the Ides of March), while the
fact that Brutus stabbed Caesar is something abstract and
non-spatiotemporal. The question then arises as to whether causation
requires immanent or transcendent relata.

The second main differentiator that one finds invoked is
individuation. Events are sometimes (though not always) held
to be relatively coarse-grained, while facts and the others are held
to be relatively fine. For instance, the event of John's saying
“hello” may be reckoned the same as the event of John's
saying “hello” loudly, while the fact that John said
“hello” is different from the fact that John said
“hello” loudly. The question then arises as to whether
causation requires coarse or fine relata.

Fortunately, questions of the true metaphysics of events, facts, and
the other candidates may be postponed here, and the questions of the immanence
and individuation of the causal relata may be addressed directly.
Thus the issue of the category of the relata may, in practice, be
usefully replaced by two questions: whether the relata are immanent (Section
1.1), and how finely they are individuated (Section 1.2).

Number and Role: What are the number and role of the
causal relata? How many causal relata are there, and what kind of job
do they do? An account of the number and role of the relata should
first formulate general determinants of the adicity of relations, and
then apply these determinants to causation.

The view that there are two relata is widely assumed but seldom
defended. Three main alternatives have been explored involving
contrastivity. The first of these alternatives, inspired by van
Fraassen's (1980) work on contrastive explanation, takes causal
relations to include an effectual difference. On this view
causal relations have the form: c causes e rather
than e*. The second main alternative, based on Hitchcock's
(1993, 1995a, 1996) work on probabilistic causation, takes causal
relations to include a causal alternative. On this view
causal relations have the form: c rather than c*
causes e. The third main alternative, defended by Schaffer
(2005), includes both a causal alternative and an effectual difference
and so numbers the causal relata at four, yielding the form:
c rather than c* causes e rather than
e*. The question then arises whether contrasts (for cause
and/or effect) help resolve problems and paradoxes (Section 1.3).

Three further main alternatives have been explored positing secondary
relata. The first of these, inspired by Anscombe's (1975) claim that
causation is an intensional relation, takes causation to be relative
to descriptions of the primary relata. On this view, causal relations
have the form: c causes e relative to D,
where D is an ordered pair of descriptions (for c
and for e). The second of these alternatives, arising
especially from Pearl's (2000) work on causal modeling, treats
causation as relative to a certain sort of mathematical
representation. On this view, causal relations have the form:
c causes e relative to M, where M
is an apt causal model of the situation. The third of these
alternatives, which has roots in Hart and Honore's (1985) treatment of
causation in the law, treats causation as relative to default states,
which encode the states that are considered “normal” and
“natural,” as opposed to the deviant states. The simplest
version of this view runs: c causes e relative to
N, where N is an ordered pair of natural outcomes
(concerning c and e). These views are all
compatible. One could for instance hold that causal relations have the
form: c causes e relative to D, M,
and N. (Indeed one area of active research concerns the
combination of causal modeling with defaults: see Blanchard and
Schaffer (forthcoming) for a critical overview.) The question then
arises as to whether any secondary relata are needed, or whether they
all constitute an objectionable loss of objectivity, or an
objectionable departure from the allegedly “obvious
binarity” of causation (Section 1.3).

Presuppositions: Both the dispute over the category
and over the number and role of the causal relata involve
presuppositions of uniqueness. As to category, the dispute
presupposes that there is a unique category of entity from which all
causal relata must be drawn. Yet, it might be argued, ordinary
language allows for the relata to be described in eventive (imperfect
nominal), factive (perfect nominal), and other forms (Mackie 1974, Vendler 1984,
Bennett 1988). Why not take ordinary language at
its word, and let a thousand relata bloom?

As to number and role, the dispute presupposes that there is a unique
number that is the adicity. Yet, it might be argued again,
ordinary language allows for causal attributions with and without
causal alternatives or effectual differences (Hitchcock 1996). Why not
take ordinary language at its word, and let causation go
multigrade?

There are two main arguments in defense of uniqueness, the first of
which is that it staves off ambiguity (Menzies
1989a). If there were four choices for two relata, it might seem that
there would be 24=16 “causal” relations (and more if there
were more choices and/or relata and/or adicities). That said, it is
unclear why there couldn't be a single causal relation (univocally
denoted by “causation”) which allowed different types of
relata. The identity relation, for instance, can relate items of any
ontological category.

The second argument for uniqueness is that it precludes a mysterious
harmony (Mellor 1995). If there were a plurality of event
causes and fact causes and the like, some metaphysical harmony would
be needed amongst them, for surely they could not conflict. That is,
it seems that the event of the cue ball's striking the nine ball, and
the fact that the cue ball struck the nine ball, must have comparable
effects. But without a unique underlying causal relation, there would
seem to be nothing keeping these effects aligned. That said, perhaps a
plurality of causal relations could be harmonized, provided either (i)
one were fundamental and the others derivative, or (ii) all were
derivative from a common non-causal basis, such as the regularities
among the events.

Question: Are the causal relata immanent, or
transcendent? That is, are they concrete and located in spacetime, or
abstract and non-spatiotemporal?

This question is connected to the question of category. If the relata
are transcendent, then they are facts. If they are immanent, then they
are events, or one of the other candidates such as features, tropes,
or situations.

In practice, one finds three main arguments on the question of
immanence. First, there is the argument from pushing, which maintains
that the relata must be immanent so as to push things around. Second,
there is the argument from absences, which maintains that the relata
must be transcendent so that absences can figure in causal
relations. Third, there is the so-called “slingshot”
argument, which maintains that the causal relata must be immanent
events because (as per an argument from Frege) there is but one
transcendent fact: the True.

Pushing: The main argument for immanence is that
only immanent entities can interact. This argument is nicely
summarized by one of its opponents, Bennett: “Some people have
objected that facts are not the sort of item that can cause
anything. A fact is a true proposition (they say); it is not something
in the world but is rather something about the
world, which makes it categorically wrong for the role of a puller and
shover and twister and bender.” (1988, p. 22; see also Hausman
1998) According to the pushing argument, only concrete spatiotemporal
entities can be causes and effects.

There are two main responses to the pushing argument, the first of
which is to find substitute immanent entities. These substitute
immanents serve as pushers, and relate to the causal facts, while
still being distinct from them. Bennett, in the immediate continuation
of the above quote, recruits objects for just such a purpose:
“That rests on the mistaken assumption that causal statements
must report relations between shovers and forcers. I grant that facts
cannot behave like elbows in the ribs, but we know what items do play
that role — namely, elbows. In our world the pushing and shoving and
forcing are done by things — elementary particles and
aggregates of them — and not by any relata of the causal
relation.” (1988, p. 22) Mellor (1995) offers a similar response,
suggesting facta (the immanent truth-makers for facts) as the
immanent basis for fact causation.

The second response to the pushing argument is to charge that it
rests on a naive (pre-Humean) conception of causation as requiring
some sort of metaphysical push or “oomph”. If the causal
relation is a mere matter of regularity, why can't the regularities
hold between facts?

Absences: The main argument for transcendence is
that absences can be involved in causal relations. Absences
are said to be transcendent entities. They are nothings,
non-occurrences, and hence are not in the world. Thus Mellor says,
“For the ‘C’ and ‘E’ in a
true causal ‘E because C’ need not assert
the existence of particulars. They may deny it… They are negative
existential statements, made true by the non-existence of
such particulars,…” (1995, p. 132) Here Mellor is arguing
that, in the case where rock-climbing Don does not die because he does
not fall, Don's non-falling and non-dying are causally related,
without there being any events or other immanent entities to
relate.

There are two main responses to the absence argument, the first of
which is to deny that absences can be causal. In this vein, Armstrong
claims: “Omissions and so forth are not part of the real driving
force in nature. Every causal situation develops as it does as a
result of the presence of positive factors alone.” (1999, p. 177;
see also Beebee 2004a and Moore 2009) The theorist who denies absence causation
may add some conciliatory codicil to the effect that absences stand in
cause-like relations. Thus Dowe (2000, 2001) develops an account
of ersatz causation (causation*) to explain away our intuitions that
absences can be genuinely causal.

The second response to the absence argument is to deny that absences
are transcendent. One way to do this would be to accept the existence
of negative properties, and think of absences as events in which an
object instantiates a negative property. Thus Don's instantiating
non-falling at t0 might be counted an immanent
event, and a cause of the further immanent event of his instantiating
non-dying at t1. A second way to deny that
absences are transcendent would be to take absence claims as merely a
way to describe occurrences, as Hart and Honore recommend: “The
corrective here is to realize that negative statements like ‘he
did not pull the signal’ are ways of describing the world, just
as affirmative statements are, but they describe it by
contrast not by comparison as affirmative statements
do.” (1985, p. 38) Thus Don's not falling at
t0 may be identified with his clinging to the rock
at t0, and Don's not dying at
t1 may be identified with his surviving at
t1, which events are indeed causally related.

Slingshot: Davidson's argument for immanence is the
slingshot, which is an argument (from Frege) that there is
only one fact, the True. Briefly stated, the argument runs as
follows. First, let f1 and f2
be any true facts. Then f1 is logically equivalent
to the fact that {x: x=x &
f1} = {x:
x=x}. Moreover, {x: x=x
&
f1} is extensionally equivalent to {x:
x=x &
f2}, and so by substitution f1
is logically equivalent to the fact that {x:
x=x &
f2} = {x: x=x}. But
that is logically equivalent to f2, and so
f1 and f2 (our arbitrarily
chosen true facts) are logically equivalent. If all facts were indeed
logically equivalent, they would, of course, be unsuited for being
causal relata. (Davidson 1980b)

The main defense against the slingshot is to block some of its
substitution principles (see Mackie 1974, Menzies 1989, and Mellor
1995). One might reject the logical equivalence of
f1 with the fact that {x:
x=x &
f1} = {x: x=x}. Or
one might deny that substituting the extensional equivalents
{x: x=x & f1} and
{x: x=x & f2}
inside the context ‘…the fact that…’ preserves
logical equivalence.

A more conciliatory version of this defense is to maintain that there
is still a coherent conception of facts shielded from the
slingshot (Bennett 1988). That is, one might distinguish between
facts1, defined so that the substitutions of the
slingshot are valid, and facts2, defined so that
at least some of these substitutions are invalid. Then facts conceived
of as facts2 may still serve as the causal relata.

Question: How are the causal relata individuated?
That is, if r1 and r2 are
causal relata, what are the conditions that determine whether
r1=r2?

This question is related to the question of category. If the relata
are coarse-grained, then they are events of a certain stripe. If they
are fine-grained, then they are facts, or one of the other candidates
such as features, tropes, or situations, or else events of another
stripe.

Combining the considerations of immanence and individuation, one
might, as a first approximation, distinguish a square of possible
views underlying the dispute over category:

Coarse-grained

Fine-grained

Immanent

Davidson

Kim, Lewis, Dretske, etc.

Transcendent

[unoccupied]

Bennett, Mellor

In the upper-right quadrant one finds, alongside fine-grained events
theorists such as Kim and Lewis, virtually all those who have opted
for a third way, including Dretske, Campbell, Armstrong, Menzies, and
Paul. Indeed, virtually all the theorists who have rejected both
events and facts have done so because they think that the relata must
be immanent and thus not facts, but fine-grained and thus not events.

But the square is only a very rough first approximation, because
granularity really comes in degrees. So to a second approximation, one
might render granularity on a continuum, from the coarseness
of Davidson's (1980c) view on which the causal relata are individuated
by their causes and effects, to the moderate fineness of Kim's (1976)
view on which the causal relata are individuated by their associated
<object, property, time> triples, to the extreme fineness of
Bennett's (1988) view on which the causal relata are individuated as
finely as propositions.

The Davidson-Kim-Bennett continuum is still only an approximation
though, because there really are more occupied points along a wider
continuum. How fine-grained Kim's events actually are depends on how
finely properties are individuated. If properties are taken in an
abundant sense (individuated as finely as predicates, or at least as
finely as necessarily coextensive predicates) then Kimian events are
relatively fine-grained, whereas if properties are taken in a sparse
sense (individuated by “the joints of nature”) then the
grain is coarser. How fine-grained Bennett's facts are depends on how
finely propositions are individuated. If propositions are taken as
Frege conceives them, then Bennett's facts are exceptionally
fine-grained; whereas if propositions are taken as Russell conceives
them, then Bennett's facts are comparable in granularity to Kim's
events with abundant properties. Moreover, Davidson's view is
outflanked in coarseness by Quine's (1985; accepted by Davidson 1985)
view that the causal relata are individuated by spacetime region.
While even the Fregean variant of Bennett's view is outflanked in
fineness by Dretske's (1977) view on which even focal differences
(such as between Mary's kissing John, and Mary's kissing
John) entail differences in relata. Putting this together
yields the following picture:

Individuation: Coarse-Grained → Fine-Grained

Further discriminations along the granularity dimension are, of
course, possible.

In practice, one finds three main arguments on the question of
individuation. First, there is the argument from causal differences,
which maintains that the relata must be fine so as to mark differences
in causal relatedness. Second, there is the argument from
transitivity, which maintains that the relata must be fine so as to preserve
transitivity. Third, there is the argument from methodology, which
maintains that the relata must be coarse for general reasons of
theoretical elegance.

Causal Differences: The first main argument for
fineness is that fine differences can mark causal
differences. To take an example discussed by Davidson, it makes
sense to say, “The collapse was caused, not by the fact that the
bolt gave way, but by the fact that it gave way so suddenly and
unexpectedly” (1980b, p. 161; see also Kim 1976). This suggests
that the bolt's snapping, and the bolt's snapping suddenly, must
differ as causal relata. Or to take an example from Lewis
(1986b), John's saying “hello” must differ from John's
saying “hello” loudly, since only the former causes Fred to
greet John in return, and only the latter is caused by John's state of
tension. According to the causal differences argument, the relata must
be fine on pain of conflating conflicting causal relations.

There are three main responses to the causal differences argument,
the first of which is that “cause” is ambiguous
between causation and explanation. The causal differences
argument is said to adduce explanatory differences only (Davidson
1980b and 1980d, Strawson 1985). Davidson integrates this
response within a general account of causation and explanation, in
which causation is an extensional relation that holds between coarse
events, while explanation is an intensional relation that holds
between the coarse events under a description. So John's state of
tension causes John's saying “hello,” but the explanatory
relation only holds when the “hello” is described in terms
of its loudness. Our judgment that John's state of tension does not
‘cause’ John's saying “hello” is to be explained
away as keyed into the explanatory idiom.

The second response to the causal differences argument is that
“…causes…” is an intensional
context (Anscombe 1975, Achinstein 1975 and 1983, McDermott
1995). Intensional contexts do not license substitution of
co-referring terms salva veritate. Thus John's saying
“hello” may refer to the same event as John's saying
“hello” loudly, but substituting the one description for
the other may still change the truth-value of the causal claim. If so
then different descriptions of the same relata can induce
causal differences.

The third response to the causal differences argument is that it
overextends. It looks to require a fineness beyond what many
of its proponents have envisioned. To take an example from Achinstein
(1983), it may be true that “Socrates' drinking hemlock
at dusk caused his death,” but false that “Socrates'
drinking hemlock at dusk caused his death.” If so, the
causal differences argument entails that Socrates's drinking
hemlock at dusk, and Socrates's drinking hemlock at
dusk, must differ as causal relata. If so, then the causal
differences argument ultimately requires the extreme fineness of the
Dretskean view, which some may regard as a reductio.

Transitivity: The second main argument for fineness
is that it preserves transitivity. To adapt an example from
Woodward (1984; see also Ehring 1997, Paul 2000), suppose that
Tom puts potassium salt in the fireplace (c), Dick then
tosses a match in the fireplace, which results in a purple fire
blazing in the fireplace (d), which then spreads and
immolates Harry (e). The coarse-grained theorist looks to be
committed to the following breakdown of transitivity: Tom's putting
potassium salt in the fireplace causes there to be a purple fire
blazing in the fireplace: c causes d; there being a
purple fire blazing in the fireplace causes Harry's immolation:
d causes e; but Tom's putting potassium salt in the
fireplace does not cause Harry's immolation: c does not cause
e. The fine-grained theorist may distinguish
d1: the fire becoming purple at region r,
from d2: the fire blazing at r. Now
c causes d1 (not d2),
d2 (not d1) causes e,
and so the transitive inference to c's causing e
would be blocked.

There are two main responses to the transitivity argument, the first
of which is to bite the bullet. That is, one may accept that
c does cause e: Tom's putting potassium salts in the
fireplace does indeed cause Harry's immolation. Our intuitions to the
contrary might be written off, as above, as confusing the causal and
explanatory idioms. Or our intuitions to the contrary might be
explained away on pragmatic grounds. As Lewis remarks in a related
context, we are prone to “mix up questions of what is generally
conducive to what with questions of what caused what,” though,
“Every historian knows that actions often have unintended and
unwanted consequences.” (2000, pp. 194–5)

The second reply to the transitivity argument is to deny that
causation is transitive. There seem to be failures of transitivity
that cannot be resolved by fine-graining. For instance, to borrow an
example from Hall (2000, see also Hitchcock 2001), suppose that
the boulder begins to roll down the hill towards the hiker's head
(c), which causes the hiker to duck (d), which in
turn causes the hiker to survive (e). It seems that
c causes d and that d causes e,
yet it does not seem that c causes e or that slicing
up d into different features or aspects or whatnot will
help. If so, then transitivity is lost anyway.

Methodology: The main argument for coarseness is
that it is methodologically preferable. Quine (1985, p. 167)
charges fine-grained conceptions of the relata with invoking poorly
individuated and unfamiliar entities, and recommends extremely coarse
(spatiotemporal) individuation as principled and familiar in ontic
commitments. And Davidson (1985) embraces Quine's view as both
“neater” and “better” than even Davidson's own
(1980b) previous view.

There are two main replies to the methodology argument, the first of
which is that some of the fine-grained conceptions are perfectly
principled. Kim's (1976) fine-grained conception of events as property instantiations, for
instance, offers a precise criterion for individuation, namely:

(The generalization to n-ary relations is straightforward.)
And the entities invoked (objects, properties, and times) should be
perfectly familiar to all but the most austere nominalist. In fact,
Quine himself admits not only that Kim's fine-grained conception is
perfectly principled, but even that it “could still be
accommodated in the ontology that I have accepted.” (1985,
p. 167)

The second reply to the methodology argument is that it is not clear
that these indecencies in individuation or multiplication of entities
should count for much. As to individuation, we accept physical objects
without clear individuation principles for those, so why hold events
(or whatever the relata may be) to a stricter standard? As to
multiplication, if one has a reductive fine-grained view
(such as Lewis's 1986b view of events as transworld classes of
regions), then there is no multiplication in one's basic ontology at
all, since all the components already exist. And if one has a
nonreductive fine-grained view, then the resulting
multiplication may still be blameless. The real methodological sin is
to multiply entities without necessity, so if there is a need
for fine individuation (such as the causal differences and/or
transitivity arguments might provide), then postulation of such
entities is methodologically pure.

Question: What is the number and role of the causal
relata? That is, how many are there, and what kind of job does each
do? This question may be usefully divided into the subquestions of
whether to posit contrasts (Section 1.3.1), and whether to posit any
secondary relata such as descriptions, or models, or defaults (Section 1.3.2).

As to contrasts, one finds four main arguments. First, there is the
argument from surface form, which maintains that the causal relata
must be two to fit the surface form of utterances such as “the
short circuit caused the fire.” Second, there is the argument
from determinacy, which maintains that the causal relata must be four
for causal relations to be well defined. Third and fourth, there are
the arguments from immanence-revisited and individuation-revisited,
which maintain that the causal relata must be four to resolve the
problems about absences and causal differences reviewed above
(Sections 1.1 and 1.2, respectively).

All the arguments to be considered here call for either two or four
relata (not three). Indeed, one might argue against contrastive three
relata views that they preclude causal chains. In a causal
chain the effect at the first link serves as the cause at the
second. For this to be possible, cause and effect must be formally
exchangeable: the same structure must flank both sides of the
relation. Suppose the first domino knocks over the second, which then
knocks over the third. The binary theorist can say that c:
the toppling of the first domino, causes d: the toppling of
the second; and that d in turn causes e: the
toppling of the third domino. The quaternary theorist can say that
c rather than c*: the first domino's remaining
upright, causes d rather than d*: the second
domino's remaining upright; and that d rather than
d* causes e rather than e*: the third
domino's remaining upright. But if there were contrasts on only one
side of the relation, then no such chains could be constructed. The
links would not match.

Surface Form: The main argument for binarity is that
the surface form of causal claims reveals it. Causal claims
like “the short circuit caused the fire” make no explicit
reference to any contrasts. Such claims can be felicitously uttered
out of the blue (in discourse initial position), and so do not require
any antecedent contrast setting or presupposition fixing, either. This
is presumably the root of the idea that causation is “obviously
binary”. Indeed this sort of consideration is most prominent in
Davidson (1980b), who seeks the logical form of such surface-binary
utterances. Relatedly, Davidson rejects the nearby notion of
causal relevance because, “There is no room for a
concept of ‘cause as’ which would make causality a
relation among three or four entities rather than between two.”
(1993, p. 6)

There are three main replies to the surface form argument, the first
of which is that contrastive surface forms exist too. For instance,
one also finds such claims as “Pam's throwing the rock rather
than the pebble caused the window to shatter,” “Pam's
throwing the rock caused the window to shatter rather than
crack,” and even the combined “Pam's throwing the rock
rather than the pebble caused the window to shatter rather than
crack.” Thus surface form might seem equivocal (Hitchcock
1996).

The second main reply to the surface form argument is that surface
form may be a reduced expression of a more complex logical form. For
instance, “Ann prefers chocolate” may be used as a reduced
expression of the proposition that Ann prefers chocolate over
vanilla. Here the contrast does not need to be explicitly
articulated, or even noted earlier in the conversation. One can make
surface-binary preference claims out of the blue. So just as
preference claims might seem to have a contrastive logical form
beneath their binary surface, so causal claims too might be regarded
in this light. At any rate, as the history of semantics has shown, it
would be foolishly naive to think that ordinary language displays its
logical form on its surface. In this vein Schaffer (2012) diagnoses a
range of context-dependencies in causal discourse as being due to
implicit contrastivity.

The third main reply is to go revisionary. Even if the
logical form of causal attributions ultimately proves to be binary,
logical form should not have the last word in metaphysics anyway,
since it might predicate a property that we have theoretical reason to
reject. For instance, “The rock is moving” might seem to predicate the
property of absolute motion, but physicists have discovered that there is no
such thing. So just as motion claims only make metaphysical sense when
relativized to an inertial frame, one might think that causal claims
only make metaphysical sense when relativized to contrasts.

Determinacy: The first main argument for
quaternicity is that binary causal relations are ill
defined. Suppose that Jane smokes moderately, and develops lung
cancer. Does Jane's moderate smoking cause her lung cancer? Hitchcock
says that there is no determinate answer unless one fixes the causal
alternative: “The solution to this puzzle is to deny that there
is any such thing as the causal relevance of moderate smoking
for lung cancer… Relative to heavy smoking, it is a negative
cause of (prevents) lung cancer; relative to abstaining, moderate
smoking is a positive cause of (causes) lung cancer… Relations of
positive or negative causal relevance only hold relative to specific
alternatives.” (1996, p. 402) A parallel case could be made for
needing to fix the effectual difference. Suppose that Pablo is
choosing between blue, red, and green paint for his canvas. Does
Pablo's choosing blue paint rather than red cause the canvas to be
blue? Here one might say that there is still no determinate
answer. Pablo's choosing blue paint rather than red causes the canvas
to be blue rather than red, but does not cause the canvas to be blue
rather than green. Thus it may be concluded that contrasts are
required for both cause and effect, in order for causal claims to have
determinate truth-values.

The main reply to the determinacy argument is that binary causal
relations are well defined, after all. This reply should take the form
of applying a binary account of causation to problem cases such as the
smoking and painting cases, and simply reading off a truth-value,
whatever it may be. For instance, one might think that a
straightforward counterfactual account of causation, on which we check
whether e would still have occurred had c not
occurred, simply rules that Jane's smoking causes her lung cancer, and
that Pablo's choosing blue paint causes the canvas to be blue, full
stop.

Immanence Revisited: The second main argument for
quaternicity revisits immanence, and maintains that
additional argument places reconcile immanence with absence
causation (Schaffer 2005). The reconciliation is attempted through treating
absence-claims as setting the contrast to the associated
occurrence. For instance, “the gardener's failing to water the
flowers caused the flowers' wilting” is to be interpreted as:
what the gardener actually did (viz., the actual event of his watching
television) rather than watering the flowers (the non-actual event
that is the associated occurrence) caused the flowers to wilt rather
than blossom. And this claim may well be true. In this way, all four
of the relata may be treated as immanent entities, and absence causal
claims may still come out true. Indeed, in this way absence causation
requires no special provisions at all (which, as Dowe (2000)
explains, is not the case on virtually any binary theory).

The main reply to the immanence-revisited argument is that immanence
needs no revisiting. No reconciliation of absences and immanence is
needed, and so no additional argument places are needed. This reply
may take the form of denying immanence (that is, embracing facts),
denying that absences are causal, or maintaining that there are
immanent absences (Section 1.1).

Individuation Revisited: The third main argument for
quaternicity revisits individuation, and maintains that
additional argument places tame the causal differences argument (Schaffer 2005). The
concern is that the causal differences argument overextends, in
requiring that Socrates' drinking hemlock at dusk, and
Socrates' drinking hemlock at dusk, differ as causal
relata. The taming is attempted through treating focal differences as
contrastive differences. Thus “Socrates' drinking
hemlock at dusk” is to be interpreted as c:
Socrates' drinking Hemlock at dusk, rather than c*: Socrates'
drinking wine at dusk (or some other contextually salient alternative
to drinking hemlock); while “Socrates' drinking hemlock at
dusk” is to be interpreted as c: Socrates' drinking
Hemlock at dusk, rather than c*: Socrates' drinking hemlock
at dawn (or some other contextually salient alternative to occurring
at dusk). And these different contrasts may induce different
effects. In this way, focal differences may be allowed to yield causal
differences, without having any implications for individuation, much
less the extreme fineness of the Dretskean view.

The main reply to the individuation-revisited argument is that
individuation needs no revisiting. No taming of the causal differences
argument is required, and so no additional argument places are
needed. This reply may take the form of maintaining the Davidsonian
distinction between causation and causal explanation, of allowing that
causation is an intensional relation, or of simply accepting the
Dretskean view of the relata (Section 1.2).

As to secondary relata, one finds three main arguments. First, there
is the argument from objectivity, which maintains that any
relativization of causal relations to descriptions, models, or
defaults is incompatible with the objectivity of causation. Second,
there is the argument from the success of causal modeling techniques,
which maintains that causation must be relative to a model so that
modeling techniques may be exploited. Third, it has been argued that
default relativity provides the best explanation for our intuitions
across a range of problem cases. (The argument from surface form
(Section 1.3.1) may also serve as a fourth argument against any
secondary relata.)

Objectivity: Leaving aside linguistic issues of
surface form, the main argument against descriptions, models, and/or
defaults as secondary relata is that including these would compromise
the objectivity of causation. When the cue ball knocks the nine ball
into the corner pocket, it might seem that there is objective
causation in the world. How we choose to describe the events, model
the situation, or label certain outcomes as “default” or
“deviant” seems besides the point. For instance, if a
model M is used in which this interaction comes out as
non-causal, one might well infer, not that the interaction is
not causal relative to M, but rather that M itself
is a poor model of the real, model-independent causal facts.

There are two main (related) replies to the objectivity argument, the
first of which is to bite the bullet and deny that causation is
objective. Such a response might be partly encouraged by the thought
that causation seems to drop out of fundamental physics (2.1.2). The
second related reply is to maintain that there is still objectivity in
a wide range of surrounding notions. Thus Hitchcock invokes the notion
of token causal structure for what causal models represent,
and suggests that “we can afford to let judgments of token
causation be infected by pragmatic criteria without giving up on the
objectivity of causation generally: objectivity can be retained at the
level of token causal structure” (2007a, p. 504).

Causal Modeling: Perhaps the main argument for model
relativity begins with the success of causal modeling techniques, as
developed in Spirtes, Glymour, and Scheines (1993), Pearl (2000), and
Halpern and Pearl (2005), inter alia. These techniques have
provided working algorithms for causal discovery, and yielded elegant
accounts of type-level causal relations. It it only prudent, the
argument then begins, to seek an account of (actual, token) causation
using such techniques. Indeed it might well seem retrograde to do
otherwise. But given that different models yield different causal
verdicts, and given that there is no unique notion of a canonical
model for a given situation (at least none yet developed), it
might seem that the only remaining option is to relativize causal
relations to models (Halpern and Pearl 2005, p. 85).

There are at least three replies to the causal modeling argument to
consider. First, one might evince skepticism concerning causal
modeling. Causal modeling certainly provides an excellent account of
causal epistemology, but it is not obvious that one should draw any
metaphysical conclusions from that. Second, one might attempt to
define the notion of a canonical model. Third, one might provide an
account of causation involving existential quantification over models
(Hitchcock 2001) or even universal quantification, so as to help
oneself to modeling techniques without paying any further price in
objectivity.

Problem Cases: Perhaps the main argument for
description and default relativity, which also features as an argument
for model relativity, is the utility of such additional relata in
resolving problem cases. This style of argument covers a wide variety
of claims. Just to mention a few examples, McDermott (1995) builds
description-relativity into an overall account of causation that
enjoys a fair amount of success. McGrath (2005) has suggested that our
intuitions about which absences are causes may turn on expectations as
to which are normal. Hall (2007) has shown that certain causally
different cases may take isomorphic causal models, so that modeling
techniques may themselves require something like a default/deviant
distinction to discern these cases. And Hitchcock (2007a) uses models
with assigned default states to define up the notion of a
self-contained causal network, which he then puts to work in
addressing many of the most difficult cases in the literature. (See
Halpern and Hitchcock 2010 and forthcoming, as well as Blanchard and
Schaffer forthcoming, for further debate about the need for a
default/deviant distinction within causal modeling.) It is difficult
to say much more about these arguments in general, without delving
into all the details. Obviously further consideration of these
arguments depends on detailed considerations as to how the theories in
question fare versus their rivals, and also on delicate balancing of
whether the solution proferred is worth the price of the additional
relativity.

Question: What is the causal relation? When the cue
ball knocks the nine ball into the corner pocket, what is the basis
for this causal link? An adequate account of the causal relation
should reveal where the causal lines run, which direction the causal
arrows point, and what if anything distinguishes causes from mere
background conditions. In short, it should reveal the basis for
connection, direction, and selection.

Network Model: The causal relation is typically
understood with reference to what Steward (1997; see also Beebee 2004)
calls “the network model.” The network model has two main
components. First, it pictures the causal relation as a directed
segment, and the causal relata as nodes. Second, the network model
pictures history as a vast causal network. On the network model, given
some realistic assumptions, the causal history of e forms a
vast inverted tree (though one which ultimately narrows back down to
the big bang):

An account of connection is an account of the segments; an account of
direction is an account of the arrowheads. Selection on the network
model would consist in highlighting certain nodes:

The network model without selection is implemented, for instance, in
the neuron diagrams popularized by Lewis. In neuron diagrams, circles
doubly represent neurons that fire and events that occur, and arrows
doubly represent synapses that stimulate and causation that
obtains.

The network model without selection is also implemented in the
directed acyclic graphs used in causal modeling to partially visualize
the models (Spirtes, Glymour, and Scheines 1993; Pearl 2000). In
directed acyclic graphs, nodes doubly represent variables with a range
of values and occurrences with a range of alternatives, and links
doubly represent functional determination via the structural equations
and causal parenthood. (For further explanation of causal modeling,
see the entry: causation: probabilistic.)

(Neuron diagrams and directed acyclic graphs are different
implementations of the network model, though. Neurons represent events
that occur or not: they are two-valued. Nodes represent variables that
can take two, three, or even continuously many values. Synapses
represent actual causation. Links represent lines of possible causal
influence, and do not entail any actual causation between the actual
values of their variables. See Hitchcock 2007b for comparisons and
reasons to favor the causal modeling approach.)

Connection: What is the metaphysical basis for
causal connection? That is, what is the difference between causally
related and causally unrelated sequences?

Fortunately, the details of these many and various accounts may be
postponed here, as they tend to be variations on two basic themes. In
practice, the nomological, statistical, counterfactual, and agential
accounts tend to converge in the indeterministic case. All understand
connection in terms of probability: causing is making more
likely. The change, energy, process, and transference accounts
converge in treating connection in terms of process: causing
is physical producing. Thus a large
part of the controversy over connection may, in practice, be reduced
to the question of whether connection is a matter of probability or
process (Section 2.1).

Direction: What is the metaphysical basis for causal
direction? That is, what is the difference between sequences related
as cause to effect and those related as effect to cause or as effect
to joint effect of a common cause?

The standard view on the direction of causation is that it reduces to
the direction of time: causes occur prior to their effects (Hume
1975, Kant 1965, Beauchamp and Rosenberg
1981). The temporal view has fallen into disfavor of late, and a
number of alternatives have been suggested, for instance, that the
causal direction is the direction of forking (
Reichenbach 1956, Horwich 1987, Papineau 1993, Dowe 2000),
overdetermination (Lewis 1979), independence
(Hausman 1998), and manipulation (von Wright 1975,
Price 1991 and 1996, Woodward 2003). On these alternative
views, the coincidence of the causal and temporal orders is merely a
contingent feature of the actual world, or at least a typical feature
of our patch of it. So the question arises as to whether the causal
direction is the temporal direction, or something else (Section
2.2).

Selection: What is the metaphysical basis for causal
selection? That is, what is the difference between cause to effect
sequences involving real causes, and those involving mere background
conditions?

The standard view on selection is that there is no objective
basis for selection: selection is interest-driven, pragmatic, and
unsystematic (Mill 1846, Lewis 1986a, Mackie 1974). This
no-objective-basis view is occasionally challenged, and alternatives
have been suggested such as sufficient versus
necessary (Ducasse 1926) and abnormal versus
normal (Hart and Honore 1985). The question thus arises as to
whether there is any objective difference between “triggering
conditions” and “mere background conditions”
(Section 2.3).

Presuppositions: The dispute over the causal
connection involves a presupposition of uniqueness; there has
to be a unique metaphysical relation of causal connectedness
for there to be a question of that relation's nature. Yet, it might be
argued, ordinary language allows for a range of irreducible causal
notions, such as “scrape,” “push,”
“wet,” “carry,” “eat,” etc.
(Anscombe 1975, p. 68) Why not take ordinary language at its word, and
adopt a form of causal pluralism on which ‘cause’ is
viewed as providing a merely nominal grouping of metaphysically
diverse relations?

One might defend uniqueness by arguing that scraping, pushing,
wetting and the others have a real (more than nominal) unity. They
have common statistical, counterfactual, predictive, explanatory, and
moral implications. Or one might defend uniqueness as a theoretical
ideal. Even if our actual concept of causation is ultimately what
Skyrms (1984) calls an “amiable jumble” of principles
(see also Sober 1985, and Hall 2004), this might be
taken as a call for conceptual revision. Why wallow in the jumble,
instead of tidying it?

Question: What is the basis for causal connection?
Is it a matter of probability, process, or some hybrid thereof? Is
causal connection primitive and irreducible? Or is the entire notion merely a folk myth?

The probability and process views appear subject to a number of
systematic problems, including the problems of preemption and
fizzling for probability views, and disconnection
and misconnection for process views (Section 2.1.1). These
problems force the views to evolve and might be seen as motivating the
hybrid, primitivist, and eliminativist alternatives (Section
2.1.2).

Preemption: One problem case for the probability
view, on which the root idea of causation is that of making more
likely, is the case of preemption (Good 1961 and 1962, Lewis
1986a, Menzies 1989b, Collins, Hall, and Paul 2004, Paul and Hall 2013
inter alia). Suppose that Pam and Bob each aim a brick at a
window. Pam throws and shatters the window, while Bob holds his throw
on seeing Pam in action. It seems that Pam's throw caused the window
to shatter — her brick is what crashes through the glass. But it
does not need to be the case that Pam's throw raised the probability
of the shattering — if Bob is a more reliable vandal, then Pam's
throw might even have made the shattering less likely. So it
seems that probability-raising is not necessary for causation.

This sort of preemption (an early cutting) can be
represented by the following neuron diagram:

A filled circle doubly represents a neuron firing and an event
occurring. The line with a circular arrowhead doubly represents an
inhibitory connection and a prevention.

Probability theorists have responded to preemption with three main
strategies, the first of which is to factor intermediaries
(Lewis 1986a, Menzies 1989, Eells 1991, Ramachandran 1997, Kvart 1997,
Noordhof 1999, Pearl 2000, Yablo 2002). This approach looks to the
course of intermediary events or probability evolutions to find some
sense in which the preempting cause is indeed a
probability-raiser. For instance, if one holds fixed the fact that Bob
holds his throw, then it might seem that Pam's throwing becomes a
probability-raiser after all. The second response that probability
theorists offer to preemption is to require precision (Rosen
1978, Lewis 1986a, Paul 2000, Coady 2004). This approach looks to the
exact time and manner of the events involved to try to find
differences due to the preempting cause. For instance, if one
considers the exact time and manner of the window shattering, then it
might seem that Pam's throwing was a probability-raiser all along. The
third response is to consider intrinsic structure (Lewis
1986a, Menzies 1996, Hall 2004) This approach looks to the intrinsic
structure of the preempting process to try to find some sense in which
the preempting process — even if it does not itself involve
probability-raising — is at least intrinsically right for
probability-raising.

It is unclear how far these three strategies extend. There is a
vast literature on preemption involving a dizzying array of varied
counterexamples and revised analyses. See Paul and Hall for an
excellent guide to the “thick undergrowth of such
examples” (2013, p. 5). It is fair to say that no currently
available account is able to handle every case.

For a particularly difficult case, it has been argued that there can
be preemption with no intermediaries to factor or differences to be
precise about or intrinsic failure of the preempted backup, in cases
of trumping (Schaffer 2000a, Lewis 2000). Suppose that the
laws of magic say that the first spell cast on a given day matches the
enchantment that midnight. Merlin casts a spell (the first that day)
to turn the prince into a frog, Morgana casts a spell (the second that
day) to turn the prince into a frog, and at midnight the prince turns
into a frog. It seems that Merlin's spell caused the prince to turn
into a frog — his spell was the first cast that day, and that's
what the laws of magic identify as the relevant feature. Only Merlin's
spell satisfies the antecedent conditions of the imagined law of
nature. But it does not need to be the case that Merlin's spell raised
the probability of the enfrogging — if Morgana is the more
reliable wizard, then the chance of the enfrogging would have been
greater has Merlin left the job to Morgana. It does not need to be the
case that there are any intermediary events at all in the story
— the magic might as well work directly. And it does not need to
be the case that there would have been any differences in what befalls
the prince had Merlin left it to Morgana. And finally, there does not
seem to be any difference in “intrinsic aptness” between
Merlin's and Morgana's spell. In fact the only relevant difference
between these spells seems to be the extrinsic matter of which was
cast first.

This sort of trumping preemption can be represented by the following
neuron diagram (Paul and Hall 2013):

Here we suppose that neurons can fire in various colors (representing
various possible spells), and that by law, when a neuron receives
multiple stimulations, it fires in the color matching that of the
biggest neuron (representing the first spell that day) stimulating
it.

A third response that some probability theorists have advocated is to
bite the bullet. Here it might be maintained that the effect occurred
not because of, but despite, the preemptor (Eells 1991,
Mellor 1995). Or it might be maintained that, at least in certain
cases, the “preempted backup” is actually an
overdetermining cause. For instance, Hitchcock (2011) argues that a
contrastive approach to causation allows one to capture much of the
intuitive asymmetry of trumping cases, while still counting the
trumped event (Morgana's spell) as an overdetermining cause of the
outcome (the prince becoming a frog).

Fizzling: A second problem case for the probability
view is fizzling. Suppose that Pam and Fred each aim a brick
at a window. Pam throws and shatters the window, while Fred simply
walks away, or throws wide, or is preempted by Pam. It seems that
Fred's aiming did not cause the window to shatter — Fred's brick
never touched the glass. But it might be the case that Fred's aiming
did raise the probability of the shattering — if there was some
non-zero chance that Fred would succeed, and some non-one chance that
Pam would succeed, then Fred's aiming might well have placed the window in
greater danger. So it seems that probability-raising is not sufficient
for causation.

The version of fizzling in which Fred is preempted can of course be represented
by the early cutting neuron diagram above, with Fred standing in for
Bob.

Probability theorists have responded to fizzling with the same
strategies as for preemption, namely factoring intermediaries,
requiring precision, or looking at intrinsic aptness (Menzies 1989b,
Hitchcock 2004, Kvart 2004). For instance, if one holds fixed the fact
that Fred throws wide, then it might seem that Fred's throwing is not
a probability-raiser after all. Or if one considers the exact time and
manner of the window shattering, then it might seem that Fred's
throwing was not a probability-raiser after all. Or if one looks at
the intrinsic character of the Fred process, then it might seem as if
this process was intrinsically not apt to cause the window
shattering.

It is unclear how far these three strategies extend. One might think
that there can be fizzlings with no intermediaries to factor or
differences to be precise about or intrinsic defectivness of the
fizzled non-cause, in cases of overlapping (Schaffer
2000b). Suppose that Merlin casts a spell with a .5 chance of turning
the king and prince into frogs; Morgana casts a spell with an
independent .5 chance of turning the prince and queen into frogs; and
the king and prince, but not the queen, then turn into frogs. It seems
that Morgana's spell did not cause the prince to turn into a frog
— the fact that the queen was unaffected shows that Morgana's
spell fizzled. But it is the case that Morgana's spell raised the
probability of the prince turning into a frog. Moreover it need not be
the case that there are any intermediary events in the story at all
(the magic might as well work directly). It need not be the case that
there would have been any differences in what befalls the prince had
Morgana's spell taken hold rather than Merlin's. And it need not be
the case that Morgana's spell was intrinsically defective in any way
(indeed it is only the external circumstance of the queen being
unaffected that reveals that Morgana's spell fizzled).

This sort of overlapping case can be represented by the following
neuron diagram:

Here an arc with a number represents a conjunctive effect with a
certain probability.

Preemption and fizzling cases together might be taken to show that
probability-raising (however interpreted and refined) is
systematically unable to provide necessary or sufficient conditions
for causation. Moreover, these cases might suggest that connection is
a matter of processes (be they physical or magical) rather than
probabilities. The preempting cause and the effect are linked by a
process, while the fizzled non-cause and the effect are not —
just look at the diagrams. As Armstrong writes: “Where there is
an arrow in a diagram showing that one neuron brings it about that
another neuron fired, or is rendered incapable of firing, take it that
here there is a genuine two-term relation of singular causation
holding between cause and effect. Where there is no such arrow, deny
that there is any such relation. This is the open door” (2004,
p. 446).

But the process view faces problem cases of its own.

Disconnection: One problem case for the process view,
on which the root idea of causation is that of physical connection, is
disconnection (Ehring 1984, Schaffer 2000c, Lewis 2004, Hall
2004). Suppose that Pam catapults her brick through the window rather
than throwing it. Then it seems that Pam's catapulting the brick
causes the window to shatter — can it really matter here whether
Pam catapults the brick or throws it? But there need be no process
connecting Pam's releasing the lever and the flight of the brick
through the window — no relevant energy-momentum flow, track of
mark transmission, or persisting trope connects them. Rather what is
happening here is that the cocked catapult is prevented from launching
by the catch, and Pam's releasing the lever prevents the catch from
preventing the launch — the catapult is thus unleashed. The
process of launch is purely internal to the catapult.

This sort of disconnection case can be represented by the following
neuron diagram:

The main reply that is made to disconnections is to deny that they
are genuinely causal. In this vein, Aronson says: “Consider a
weight that is attached to a stretched spring. At a certain time, the
catch that holds the spring taut is released, and the weight
immediately begins to accelerate. One might be tempted to say that the
release of the catch was the cause of the weight's acceleration. If
so, then what did the release of the catch transfer to the weight?
Nothing, of course.” (1971, p. 425; see also Dowe 2001, Hall
2004) Indeed, since disconnections look to involve preventions
of would-be-preventers, and since prevention looks to involve
absences, one might reject causation by disconnection for the general
reason that there is no absence causation (Moore 2009). For instance, one might
deny that any causal connection can run through the absence of the
catch.

Misconnection: A second problem case for the process
view is misconnection (Hitchcock 1995b, Dowe 2000, Schaffer
2001). Suppose that Pam throws her brick through the window, while
innocent Tom watches in dismay, or sprays purple paint in the air
through which Pam's brick passes. Then it seems that Tom's watching or
paint-spraying does not cause the window shattering. But there is a
process connecting Tom's watching or paint-spraying to the
shattering. When Tom watches there will be photons connecting him to
the shattering. When Tom sprays paint at the brick there will be a
track of purple paint from Tom's spray can to the brick to the window.
(Misconnections might be subdivided into micro-connections,
which are of the wrong magnitude such as the photons, and
pseudo-connections, which are of the wrong sort such as the
paint.)

One finds two main replies to misconnections in the literature, the
first of which is to bite the bullet. In the case of the photon
connection from Tom's watching to the window shattering (and
micro-connections generally), this might be regarded as causation of
such negligible proportions that it is understandable that we might
neglect it. Our intuitions to the contrary might also be written off,
Davidson style, as confusing the causal and explanatory idioms.

The second main reply one finds to misconnections is to fine-grain the
processes involved. In the case of the paint connection from Tom's
spraying to the window shattering, the line of paint persistence and
the line of brick flying through the window might be regarded as
distinct and merely coincident (Dowe 2000). In this way it might be
denied that there is a genuine process connecting the misconnecting
non-cause and the effect.

Disconnection and misconnection cases together might be taken to show
that process-linkage (however interpreted and refined) is
systematically unable to provide necessary or sufficient conditions
for causation. Moreover, these cases might suggest that connection is
a matter of probabilities rather than processes. The disconnecting
cause (such as Pam's release of the catapult) and the effect are
linked by probability, while the misconnecting non-cause (such as
Tom's bystanding or spray painting) and the effect are not. So the
probability theorist might claim revenge. But one might also draw the
larger moral that the probability and process views are at best
aspects of a bigger picture. This might inspire the search for a
hybrid view.

Hybrids: Given the intuitive plausibility of the
probability and process views, and the systematic problems each
encounters, some recent theorists have sought reconciliation. Hybrid
views aim to synthesize the probability and process views, capturing
what is intuitively right about both ideas while resolving their
problem cases.

The most obvious hybrid views simply conjoin or disjoin the
probability and process views, or posit an ambiguity between the
notions (Hall 2004). With respect to the above four problem cases,
however, this might seem unpromising. Requiring both probability and
process will resolve fizzlings and misconnections (Salmon 1997), as
the former involves no process-linkage and the latter no
probability-raising. But for the same reason it will not resolve
preemptions and disconnections, as the former involves no
probability-raising and the latter no process-linkage. (The
conjunctive theorist might still avail herself of one of the above
replies to preemption and disconnection.) Likewise requiring either
probability or process will resolve preemptions and disconnections,
but not fizzlings and misconnections. (The disjunctive theorist might
still avail herself of one of the above replies to those
problems.)

More sophisticated hybrid views attempt to integrate the
notions of probability and process, and not merely conjoin or disjoin
them. Thus Fair (1979) ultimately moves from an energy flow view to a
view that understands connection in terms of counterfactuals about
energy flow. And Schaffer (2001) suggests a generalization of this
approach, on which causal connection is understood in terms of the
probabilities of processes. This sort of hybrid view might seem to
resolve all of the above problem cases. The preempting cause and
disconnecting cause do raise the probability of the process that
produces the effect; the fizzled non-cause and misconnecting non-cause
do not.

However this sort of hybrid view has trouble with “hybridized”
problem cases such as the following (Schaffer 2001). Suppose that Pam
throws a brick through the wall of an aquarium, preempting Bob from
doing the same. The aquarium shattering then causes the soaking of the
carpet, by preventing the glass from preventing the water from
spilling. This is a preemption case fed into a disconnection case. It
seems that Pam's throw caused the soaking of the carpet — her brick
is what broke the aquarium. But it need not be the case that Pam's
throw raised the probability of the process producing the soaking —
if Bob is a more reliable vandal, then Pam's throw might have even
lowered the chance of the spillage process, by preempting Bob. And it
might also be the case that Bob's aiming raised the probability of the
process producing the soaking — Bob's aiming might have raised the
chance of the spillage process, by threatening the aquarium.

(Such a case also makes trouble for the Hall style “two
concepts” view, since Pam's throw turns out to satisfy
neither of the two concepts of causation Hall reports.) This
sort of preemptive disconnection case can be represented by the
following neuron diagram:

The current literature on causation is now suffused with complex
hybrid cases, including cases of preemptive prevention (McDermott
1995, Collins 2000), disconnections inside larger chains (Hall 2004),
and a variety of devious preemption variants (Paul and Hall 2013). No
known account of causation — hybrid or otherwise — gets
all of these cases right. So it is unclear what hybrid accounts gain
in the end.

Primitivism: The problems encountered by attempts to
analyze causal connection provide one main argument for
primitivism. There seems to be a pattern of failure, which might
suggest that causation is simply unanalyzable.

The second main argument for primitivism is that causation is too
central to reduce. The probability and process accounts (and by
extension hybrids) are said to be inevitably circular, because the
notions of probability and process cannot be understood without
reference to causation. As to probability, each of the nomological,
statistical, counterfactual, and agential versions of the theory might
be thought to harbor causal notions. The causal relation might be
required to distinguish real laws from accidental generalizations
(Armstrong 1997), to distinguish which background conditions must be
held fixed in statistical assessment from which may vary (Cartwright
1983), to distinguish which background conditions may be held fixed in
counterfactual supposition from which may vary (Kvart 1986), and to
understand the notion of agential intervention (Hausman 1998). As to
process, it might be thought that a process is nothing more than a
causal sequence; in the words of Sayre: “The causal process,
continuous though it may be, is made up of individual events related
to others in a causal nexus… It is by virtue of the relations
among members of causal series that we are enabled to make the
inferences by which causal processes are characterized.” (1977,
p. 206)

Indeed, the primitivist might add that the notion of event (or
whatever the causal relata is taken to be) cannot be understood
without reference to causation, because properties themselves are
individuated by their causal roles (Shoemaker 1980 and 1998,
Ellis 1999). As Carroll remarks in this regard,
“With regard to our total conceptual apparatus, causation is at
the center of the center.” (1994, p. 118) So one might think that
analysis is impossible because we have no more basic concepts.

As a third main argument for primitivism, it has been argued that
there are worlds that differ purely causally (Armstrong 1983, Tooley
1987, and Carroll 1994). Suppose that it is a law of magic that all
spells have a .5 chance of taking hold, that Merlin and Morgana each
cast a spell to turn the prince into a frog at midnight, and that the
prince turns into a frog at midnight. Then it may be intuited that
there are three distinct possibilities: one in which only Merlin's
spell caused the enfrogging, a second in which only Morgana's spell
did it, and a third in which both did. These possibilities feature the
same laws and pattern of events. So one might claim to intuit that
causation is ontologically fundamental.

But there also three main arguments against primitivism, the first of
which traces back to Hume and maintains that primitivism conflicts
with the existence of causal knowledge. After all, one might argue (in
a Humean vein) that all we can observe are sequences of events; as such, we
could never come to know any facts about causal connection if
connection is anything over and above such sequences. To this the
primitivist might reply, either that primitive connections can be
directly observed, at least in certain favorable cases such as willing
or pressure on the body (Anscombe 1975, Strawson 1985, Fales
1990, Armstrong 1997); or that primitive connections can be
theoretically inferred via inference to the best explanation (Tooley
1987).

The second main argument against primitivism is that primitive
causation is a spooky sort of primitive modality. To the extent that
causal relations are supposed to be necessary connections in
nature, and to the extent that one generally favors the reduction of
the modal to the occurrent, one will have a general reason to resist
any causal primitivism.

The third main argument against primitivism is that it leads to
eliminativism. For if the options are irreducible causation or none,
one should ask whether ‘none’ might be the better
choice. For if science provides the criterion for which basic
contingent entities one ought recognize, then the question must arise
as to whether one could do science without any causal primitive
whatsoever. One might conclude that our folk notion of causation must
either reduce or face elimination.

Eliminativism: The final view of causal connection
to consider is the eliminativist view, as trumpeted by Russell:
“The law of causation,… is a relic of a bygone age,
surviving, like the monarchy, only because it is erroneously supposed
to do no harm.” (1992, p. 193) The eliminativist views the
causal concept as a naively animistic projection of agency onto the
world, to be superseded in a sophisticated scientific scheme.

The main argument for eliminativism is that science has no need of
causation. The notion of causation is seen as a scientifically
retrograde relic of Stone Age metaphysics. As Russell claims, “In
the motions of mutually gravitating bodies, there is nothing that can
be called a cause, and nothing that can be called an effect; there is
merely a formula.” (1992, p. 202, see also Quine 1966) The
differential equations of sophisticated physics are said to leave no
room for causes, or at least to have no need of them.

Russell's argument might be effective against a primitivist
treatment of causation, but the reductivist may reply that causation
still reduces to scientifically respectable entities. In this respect,
‘event,’ ‘law,’ ‘cause,’ and
‘explanation’ are in the same boat. These nomic terms
serve to allow a systematic understanding of science; they do not
themselves appear in the equations. From this perspective, Russell's
argument might seem akin to the foolish claim that math has eliminated
the variable, because the term ‘variable’ does not appear
in the equations!

The main objection to eliminativism is that causation is too central
to eliminate. Causation, according to various contemporary
philosophers, is required for the analysis of metaphysical concepts
such as persistence, scientific concepts such as explanation and
disposition, epistemic concepts such as perception and warrant,
ethical concepts such as action and responsibility, mental concepts
such as functional role and conceptual content, and linguistic
concepts such as reference. Elimination is not just unjustified; it
would be catastrophic. So it might seem that the arguments against
primitivism and eliminativism bring one back to a reductive account of
causation, and thus back again to probability and process, and their
descendants.

Though perhaps there is some middle ground between the hopeless
task of conceptual analysis on the one hand, and the conceptual
disaster of primitivism/eliminativism on the other. For one should not
confuse the prospects for conceptual analysis with the prospects for
ontic reduction. It could well be that our concept of causation
— something in the mind — is not definable via other
concepts (in any way that would count as an informative conceptual
analysis). Yet it could also be that the causal relation — an
entity out in the world — is not a fundamental constituent of
reality. This middle position would claim to explain both the failures
of conceptual analyses, and the disappearance of causation from
fundamental physics. (See Schaffer 2007, pp. 872–873) for some further
discussion.)

Question: What is the basis for causal direction? Is
it a matter of temporal direction, or something else such as the
direction of forking, the direction of overdetermination, the
direction of independence, or the direction of manipulation? Is
causal directedness a primitive, irreducible affair? Or is the belief
in causal directedness merely a folk myth, or perhaps a projection of
our experience as human agents onto an undirected world?

In practice, one finds six main arguments on the question of whether
to identify causal direction with temporal direction. First, there is
the argument from bilking, which maintains that the causal
order must be the temporal order, or else the effect might occur but
the cause then get prevented. Second, there is the argument from
time travel, which maintains that the causal order must not
be the temporal order because of the possibility of time
travel. Third, there is the argument from simultaneous
causation, which maintains that the causal order must not be the
temporal order because of the possibility of cause and effect being
contemporaneous. Fourth, there is the argument from joint
effects, which maintains that it will not help to analyze the
causal order as the temporal order because there are joint effect
cases in which there is a temporally ordered connection without
causation. Fifth, there is the argument from physics, which
maintains that the causal order must not be the temporal order because
of various physical hypotheses involving backwards causation. Sixth,
there is the argument from the causal theory of time, which
maintains that the causal order is the temporal order, but only
because the temporal order is to be analyzed in terms of the causal
order, not vica versa.

Bilking: The main argument for the causal order
being the temporal order is the bilking argument (Black 1956). The
argument is explained by Mackie, with reference to a backward causal
hypothesis that a drawing made by an alleged clairovoyant on Monday
might be caused be a pattern made Tuesday: “But on every
occasion, after the drawing is made, it is possible that someone or
something should intervene so that the corresponding pattern fails to
be produced. Consequently, it cannot on any occasion be the pattern
that is responsible for the details of the drawing: the precognition
hypothesis must be false even for those occasions when the device is
not stopped, when the pattern is actually produced and turns out to be
just like the drawing.” (1974, p. 178) So temporally backwards causation is
said to be impossible.

There are two main replies to the bilking argument. The first, due to
Dummett (1964), is to note that the argument only applies to
cases in which human intervention is possible. What is there to
prevent backwards causation when human intervention is ruled out?

The second main reply to the bilking argument is that it involves an
incoherent mix of determinism and indeterminism. If the world is
deterministic, then the bilking intervention is impossible, as it will
already be fixed that the later cause will occur. If the world is
indeterministic, then the bilking intervention is possible but no
longer problematic, as the case will then reduce to one in which the
earlier event (e. g., the clairvoyant's drawing) is an uncaused
indeterministic eruption.

Time Travel: The first main argument against the
causal order being the temporal order is that temporally backwards causation is
possible in cases such as time travel. It seems
metaphysically possible that a time traveler enters a time machine at time
t1, thus causing her to exit the time machine at
some earlier time t0. Indeed, this looks to be
nomologically possible, since Gödel has proved that there
are solutions to Einstein's field equations that permit looping
pathways: “By making a round trip on a rocket ship it is possible
[in worlds governed by Einstein's field equations] to travel into any
region of the past, present, and future and back again, exactly as it
is possible in other worlds to travel into distant parts of
space.” (1949, p. 560)

There are three main replies to the time travel argument. The first
reply is that time travel is incoherent. A variety of
incoherencies might be alleged here, including the incoherency of
changing what is already fixed (causing the past), of being both able
and unable to kill one's own ancestors, or of generating a causal loop
and thus a reflexive relation of “self-causation”, or of
generating inconsistent probability assignments (Mellor 1995). The
Gödelian proof might be dismissed as a mere mathematical
artifact, not reflecting any possible situation.

The second reply to the time travel argument is that time travel may
still take place through locally forward causal steps.
Indeed, this is exactly what happens in the nomologically possible
cases discovered by Gödel; spacetime is topologically structured
in such a way that a series of locally forward steps produces a
globally backwards path. This is compatible with the causal order
being the temporal order, at least at each particular step. It may be
that both the causal order and the temporal order can fail to possess
global orientation.

The third reply to the time travel argument is that any alleged case
of time travel is open to forward redescription. Instead of
the time traveler entering the machine at t1 and
exiting at t0, the same situation may be
redescribed in terms of the spontaneous creation at
t0 of one individual, and the spontaneous
disappearance at t1 of another, with merely
coincidental correlations between their various mental and physical states.

Simultaneous Causation: The second main argument
against the causal order being the temporal order is that
simultaneous causation is possible. Indeed, it might seem
that simultaneous causation occurs in the actual world, for instance
when an iron ball depresses a cushion (Kant 1965, Taylor 1966,
Brand 1980).

The main reply to the simultaneous causation argument is that the
cases appearing to exemplify it are misdescribed (Mellor
1995). The iron ball takes time to depress the cushion, and in general
all bodies take time to communicate their motions. There are no
perfectly rigid bodies, at least in any nomologically possible
world. Without the intuitive support of this sort of case, the
simultaneous causation argument may be charged with begging the
question. At this point methodological issues about the relevance of
conceivable but physically impossible cases may arise.

Physics: The third main argument against the causal
order being the temporal order is the argument from physics.
Physicists of the past century have entertained a variety of theories
positing backward causation, including the Wheeler-Feynman theory of
radiation, Feynman's tachyon theory and his theory of positrons as
electrons moving backwards in time, and de Beauregard's “quantum
handshake” explanation of the violation of the Bell inequalities. While none of
these theories enjoys much credence today, that they were serious
physical hypotheses (at least once) seems to establish that they at
least might have been true (Horwich 1987, Dowe 2000).

There are two main replies to the argument from physics, the first of
which is to dismiss these theories. Perhaps these theories
are all in the end false or even subtly incoherent. Here the
possibility of forward redescription alluded to with time travel is
salient, in that the defender of the temporal order may hold that
forward redescription is always possible, and always preferable.

The second reply to the argument from physics is that it
overextends. There may be no coherent account of the causal
order compatible with all these theories. In particular, the backwards
causal model of the violation of the Bell inequalities postulates a backwards causal
arrow that, it would seem, is neither the tine of a past-open fork,
nor a special overdeterminer of the future, nor a handle to manipulate
the past. So the argument from
physics might culminate in a general tu quoque.

A different sort of argument from physics looks not to theories
positing backwards causation, but rather to the lack of any relevant
asymmetries (temporal or otherwise) in advanced physics. From this it
is inferred that reality itself may be temporally symmetric, and that
any sense of a direction to causal relations is due to a
projection of our experience as agents (Price 1996 and
2007). Alternatively it might be argued that physics does supply a
real direction — perhaps via Albert's “Past
Hypothesis” (Albert 2000, Loewer 2007, Kutach 2007) — but
one that is only contingently connected to the direction of time.

Joint Effects: The third main argument against the
causal order being the temporal order is the problem of joint effects
(Lewis 1986a). Suppose that the fall in atmospheric pressure at
t0 causes both the dip in the barometer at
t1 and the storm at t2. Then
the dip in the barometer and the storm are causally connected and
temporally ordered, yet this is not causation, but rather a case of
joint effects of a common cause.

This case may be represented by the following neuron diagram:

Here the left-to-right order represents the temporal order.

There are two main replies to the argument from joint effects, the
first of which is to add some further test for a joint effect
structure, such as the screening off test (Reichenbach 1956,
Suppes 1970, inter alia). The causal direction is then taken
as the unscreened temporal direction.

The second main reply to the argument from joint effects is to
restrict the temporal order view to cases of direct connection. As
the neuron diagram suggests, joint effects are only indirectly
connected, via their common cause (Horwich 1987). If one can identify
the direct connections and apply the temporal order to these only, one
would have an arrow from the drop in atmospheric pressure to the dip
in the barometer as well as to the storm, but no arrow from barometer
to storm. This would match the diagram.

Causal Theory of Time: A final argument to consider
is the argument that the temporal order is to be analyzed in terms of
the causal order, not vice versa (Kant 1965, Reichenbach
1956, Mellor 1981). This argument cuts both ways, in the sense that it
entails that the causal order is the temporal order (contra
the arguments from time travel, simultaneous causation, and physics),
but also entails that the causal order cannot be based on the
temporal order on pain of circularity.

The main reply to the argument from the causal theory of time is, of
course, to reject the causal theory of time. The temporal direction
will have to be understood in other terms, perhaps in terms of
intrinsic physical asymmetries such as involved with entropy or with
the decay of the neutral kaon, or perhaps simply taken as primitive
(Maudlin 2007). Though to the extent that one takes the direction of
primitive, there is a temptation to put this primitive to work to the
extent possible, including understanding causal direction.

Question: What is the basis for causal selection? Is
the distinction between real causes and mere background conditions
merely an arbitrary and unsystematic affair? Or is there a
metaphysical basis for selection having to do with sufficiency versus
necessity, abnormality versus normality, or anything else?

(It should be noted that selection is widely associated with the idea
of “the cause”. This is perhaps a mistake. We often select
multiple causes which act together. For instance, in a case of
joint causation when the four movers collectively lug the
piano up the stairs, it would be natural to select each individual
mover's efforts as a real cause of the piano reaching the second floor
(thereby selecting four real causes), all the while demoting various
factors like the presence of the staircase to the status of being
background conditions. ‘The cause’, relative to a given
context, simply refers to something like the most salient cause at the
context, just like ‘the dog’ refers to something like the
most salient dog at the context; that is all a matter of what
‘the’ means and nothing at all to do with causation, or
with dogs for that matter.)

In practice, one finds four main arguments on the question of
selection. First, there is the argument from caprice, which maintains
that our actual practice of selection is too capricious to have any
real basis. Second, there is the argument from predictability, which
maintains that our actual practice of selection is too predictable to
be without a real basis. Third, there is the argument from
inseparability, which maintains that we have no concept of causation
that subtracts selection. Fourth, there is the argument from
adicity revisited, which alleges that additional relata might
reconcile the preceding three arguments.

Caprice: The main argument for the no-basis view is
Mill's argument from caprice: “Nothing can better show the
absence of any scientific ground for the distinction between the cause
of a phenomena and its conditions, than the capricious manner in which
we select from among the conditions that which we choose to denominate
the cause.” (1846, p. 198) Mill's argument has won the field, and
is echoed by contemporary authors such as Lewis: “We sometimes
single out one among all the cause of some event and call it
‘the’ cause, as if there were no others. Or we single out a
few as the ‘causes’, calling the rest mere ‘causal
factors’ or ‘causal conditions’… We may select the
abnormal or extraordinary causes, or those under human control, or
those we deem good or bad, or just those we want to talk about. I have
nothing to say about these principles of invidious
discrimination.” (1986, p. 162) Thus selection is now generally
dismissed as groundless, and theorists seek to isolate some
pre-selected, egalitarian conception of causation.

Predictability: The main argument against the
no-basis view maintains that our selections are too predictable to be
without a basis. This point has been made by Hart and Honore, who
write: “In most cases where a fire has broken out the lawyer, the
historian, and the plain man would refuse to say that the cause of the
fire was the presence of oxygen, though no fire would have occurred
without it: they would reserve the title of cause for something of the
order of a short-circuit, the dropping of a lighted cigarette, or
lightning… In making this distinction it is plain that our
choice, though responsive to the varying context of the particular
occasions, is not arbitrary or haphazard.” (1985, p. 11)

But what could this distinction between causes and conditions be?
Ducasse maintains that it is between sufficient causes and necessary
conditions: “As a matter of established usage, ‘cause’
is contrasted with ‘condition’ in a serviceable and clearly
stated manner: The cause of a phenomenon is a change in its
antecedent circumstances which was sufficient to bring it
about. A condition of a phenomenon, on the other hand, is a
change, or more frequently a state, of its antecedent circumstances
which was necessary to its having occurred when it did.”
(1969. p. 19) But it is difficult to see how this captures our
selection of the short-circuit over the presence of oxygen, as each
factor seems necessary and neither sufficient.

Hart and Honore maintain that abnormal situations and free actions
are causes, while normal situations and non-agential factors are
conditions: “In distinguishing between causes and conditions two
contrasts are of prime importance. These are the contrasts between
what is abnormal and what is normal in relation to any given thing or
subject matter, and between a free deliberate action and all other
conditions.” (1985, p. 33) This seems to do better with respect
to the short-circuit (abnormal) versus the presence of oxygen
(normal), but at the price of such vagueness that one might think it
only verbally distinct from the no-basis view.

Inseparability: A further argument against the
no-basis view is that we have no concept of causation without
selection. As Hart and Honore put it: “The contrast of cause with
mere conditions is an inseparable feature of all causal thinking, and
constitutes as much the meaning of causal expressions as the implicit
reference to generalizations does.” (1985, p. 12, see also Schaffer 2005). The upshot of
this argument is that the no-basis view deprives us of any intuitive
grasp on the notion of cause. For how are we to judge whether or not
certain cases, such as the problem cases reviewed above or any others,
involve causation or not, if our judgments are infected with a
component of unsystematic caprice?

Lewis writes: “I am concerned with the prior question of what it
is to be one of the causes (unselectively speaking). My analysis is
meant to capture a broad and nondiscriminatory concept of
causation.” (1986a, p. 162) But it is not obvious that we
have any such concept as Lewis seeks. Or at least, it is not
obvious that our intuitions about causation can provide any
evidence concerning this “broad and nondiscriminatory
concept”, if our intuitions are shot through with selection
effects.

Adicity Revisited: A final argument to consider on
the question of selection revisits adicity (Section 1.3), and
maintains that additional causal relata might reconcile caprice and
predictability, and explain inseparability (Schaffer 2005 and
2012). What is capricious about selection is that different speakers,
in different conversational contexts, will disagree about what is a
cause and what is a background condition. If one does not know what
inquiry a speaker is pursuing, one may well find her selections
capricious. What is predictable about selection is that, once
conversational context is fixed, one can expect widespread agreement
about causes versus conditions. If one knows what inquiry a speaker is
pursuing, one will find her selections predictable. This might suggest
that what is varying capriciously is which contrasts are in play in a
given inquiry, and what is predictable is what counts as a real cause
relative to the contrasts in play.

Mackie (a binary theorist) speaks of the causal field with
reference to which causal selection is made: “A causal statement
will be the answer to a causal question, and the question ‘What
caused this explosion?’ can be expanded into ‘What made
the difference between those times, or those cases, within a certain
range, in which no such explosion occurred, and this case in which an
explosion did occur?’ Both causes and effects are seen as
differences within a field; anything that is part of the assumed (but
commonly unstated) description of the field itself will, then, be
automatically ruled out as a candidate for the role of cause.”
(1974, p. 35) The contrastivist may offer a natural implementation of
Mackie's notion of a causal field, understood now as the aspects of
the situation that are assumed present and for which alternative
(/contrasts) are not considered. This is particularly apt in
understanding selection against the backdrop of causal models, in
which only certain events are represented at all via variables (events
that are represented via variables are outfitted with a range of
alternative values, while events that are not represented at all are
not).

Causal selection, on all views, is a reflection of which alternatives
are in question. For the quaternary theorist, selection is determined
by the values of the contrast relata (including the matter of whether
any contrasts at all are being considered for a given factor). It is
thus an inseparable component of our causal concept. For the person
who thinks that causation is relative to a causal model, selection may
be determined in a comparable way by the range of events modeled by
variables (which are outfitted with a range of alternatives). On these
views the very notion of a causal connection is only well defined in
light of contrasts and/or models, and these additional relata explain
selection.

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